I want to increase the number of vertices in a cylinder
When doing most actions in 2.8+, and in the case of adding an object Shift+A there will be a menu popup, by default in the lower left portion of the screen, edit the top box, labelled vertices, to your preference.

Alternatively, in edit mode, select the top and bottom loops with alt, then use the vertex context menu by right clicking, and select subdivide on the loops.
Or with cursor in middle of cylinder press Ctrl+R move a bit with cursor until first yellow ring appears, then you can add more loops by scroll wheel or pressing number.  Enter.

Or if you just need to make cylinder look smooth, you dont have to add vertices - change shading to Smooth and in Properties Editor, Mesh Data, Normals, Auto Smooth.